Magnetic-flux propagation on a Josephson transmission line

Abstract

The propagation of magnetic flux pulses along the insulating barrier of a long Josephson junction is investigated both theoretically and experimentally. The theoretical study includes applications of both (i) the recently developed ’’inverse-scattering-transform method’’ (ISTM) to the corresponding sine-Gordon equation in characteristic (light cone) coordinates and (ii) Whitham’s method (WM) of averaged Lagrangian analysis to the sine-Gordon equation in laboratory coordinates. As the number of solitons (flux quanta) in the pulse becomes large, the ISTM becomes numerically unwieldy while WM becomes more accurate; thus these two analytical tools are complementary. WM has the advantage of being readily modified to account for small dissipative effects. Our experimental observations of magnetic-flux propagation were entirely restricted to the ’’large-amplitude limit’’ in which the average of the ac Josephson current is effectively zero. In this limit, WM indicates pulse propagation with linear dissipation. This result has been confirmed on a Josephson transmission line for which it was possible to predict pulse propagation from parameters which were measured independently on small crossed strip junctions.